Two Categories Three-dimensional Linear Code Based On Special Encoder

Theoretical knowledge of linear codes have been the object of study of algebra,information theory, cryptography and other disciplines, belonging to interdisciplinaryresearch field. Theoretical study of the linear codes, researchers have proposed anumber of encoding methods, some of the better coding scheme have beenimplemented, and widely used in the field of communications and computer networks.Currently concept, ideas and methods of enumerative combinatorics have been moreand more introduced to the study of linear coding theory which have played a certainrole for the research work.Three-dimensional linear code as an information coding model can moreappropriate simulate the real world. We need to analysis and research three-dimensionallinear code in-depth. Many ideas and methods of enumerative combinatorics have beenused to research this paper for reference.This paper first gives the specific expression of square Singleton bound of three-dimensional linear code, which encoder is an n mmatrix of square rank. Then twospecial encoders are given, which are n-dimensional vector and matrix of n2over afinite field.Classification discussion about the parity of square rank has been madein the study of the three-dimensional linear codes which generated by the n2matrix.By combining the concepts of partial order of monomial over finite field and the closedof set consisting of ternary ordered pairs, we study the codeword weight and propertiesof distance of the three-dimensional linear code which generated by these two specialencoder, and give a sufficient condition about codeword distance to achieve the squareSingleton bound. Finally, we give the description of the codeword weight correspondingto input vector fetch a specific structure type of these two types of three-dimensionallinear codes, and give a series of codewords weight inequalities.